{"paper":{"title":"Quasi-convexity of the asymptotic channel MSE in regularized semi blind estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Abla Kammoun, Karim Abed-Meraim, Sofiene Affes","submitted_at":"2013-03-16T19:19:54Z","abstract_excerpt":"In this paper, the quasi-convexity of a sum of quadratic fractions in the form $\\sum_{i=1}^n \\frac{1+c_i x^2}{\\left(1+d_ix\\right)^2}$ is demonstrated where $c_i$ and $d_i$ are strictly positive scalars, when defined on the positive real axis $\\mathbb{R}^{+}$. It will be shown that this quasi-convexity guarantees it has a unique local (and hence global) minimum.\n  Indeed, this problem arises when considering the optimization of the weighting coefficient in regularized semi-blind channel identification problem, and more generally, is of interest in other contexts where we combine two different e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4012","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}